Re: Answer is OR, why not UNION?

Originally Posted by itgl72

Still working on a test review here, havent seen this one in my home work.
x-9
--- > 0
x+7
x=9 and x=-7
Test it on the number line, end up with
(-(infinity symbol),-7) as well as (9,(infinity symbol))
Normall, I type the UNION symbol in these problems, but the answer is showing OR, so the answer shows:
(-(infinity symbol),-7) OR (9,(infinity symbol))
I don't understand this curve ball.

Re: Answer is OR, why not UNION?

Strictly speaking, the union symbol ∪ connects sets while OR connects propositions, i.e., something that can be true or false. Thus, we can write (-infinity, -7) ∪ (9, infinity). We can also write (x < -7) OR (x > 9). It is not correct to write (-infinity, -7) OR (9, infinity) and neither is (x < -7) ∪ (x > 9).

As Plato said, there is a close connection between ∪ and OR. Let P(x) and Q(x) be some propositions containing x, e.g., P(x) is x < -7 and Q(x) is x > 9. Let A be the set of all x that satisfy P(x) and let B be the set of all x that satisfy Q(x). In this example, A = (-infinity, -7) and B = (9, infinity). Then A ∪ B is the set of all x that satisfy (P(x) OR Q(x)).

This is probably beyond the scope of your course, so it's not terribly important for now.